Q10) use the accompanying graph of y = f(x)
1. What is the domain and range of f.
2. find f(-4) and f(-6).
3. find lim f(x)
x-4
4. find lim f(x)
5. Does lim f(x) exist? If it does, what is it?
6. Is f continuous at 0?
(-2,2)
(-4,1)
-6-4-2
(-6,2)
4
2
-2-
(3 marks)

Answer:

welol its in parentheses and no matter what you always do parentheses first and it shows

(24+9) and the answer to that is 33

bc your simply just adding 24+9

Step-by-step explanation:

or if your looking for something similar do

(11+22)

Answer:

46°

Step-by-step explanation:

Δ1 = 180 - 130 = 50°

Δ2 = 180 - 50 - 84 = 46°

Answer:

\(\large\boxed{\bf\:\angle \: 2 = 46^{\circ}}\)

Step-by-step explanation:

In the given triangle,

∠1 + ∠2 + 84° = 180° (angle sum property of triangles states that all the 3 angles in a triangle will sum up to 180°)

Here,

∠1

= 180° - 130° (a linear pair makes 180°)

= 50°

So, acoording to the angle sum property of triangles,

∠1 + ∠2 + 84° = 180°

∠2 + 50° + 84° = 180°

∠2 = 180° - (50° + 84°)

∠2 = 180° - 134°

∠2 = 46°

_________

Enjoy the rest of your day!

The number of students who participated in the survey, based on the histogram showing the number of hours students watch television on the weekend, is 125.

A histogram is a pictorial or graphical representation of categorical data, proportional to the frequency of a variable and whose width is equal to the class interval.

The number of students who watched between 0 - 4 hours = 20

The number of students who watched between 5 - 9 hours = 40

The number of students who watched between 10 - 14 hours = 30

The number of students who watched between 15 - 19 hours = 20

The number of students who watched between 20 - 24 hours = 15

The total number of students who participated = 125

Thus, using the histogram, the total number of students who participated in the survey was 125.

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A transformation would accomplish this include the following: C. a rotation 180° counterclockwise about the origin.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point X (0, 4)  →  Coordinates of point Y = (0, -4)

Coordinates of point X (1, 3)  →  Coordinates of point Y = (-1, -3)

In conclusion, we can logically deduce that this transformation rule (x, y) → (-x, -y) would map Figure X onto Figure Y.

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Step-by-step explanation:

the number of students =24

number of boys =8

to have in fraction

8/24 = 1/3

The requried, 20 youths use both iPhone and Samsung, and 200 youths use neither iPhone nor Samsung.

Let A be the set of youths using only iPhones, B be the set of youths using only Samsung, and C be the set of youths using both. Then, we have:

|A| = 150

|B| = 770

|A ∪ B| = 900

We want to find |C| and |A ∩ B| (which is the number of youths using both).

Using the inclusion-exclusion principle, we have:

|A ∪ B| = |A| + |B| - |A ∩ B|

900 = 150 + 770 - |A ∩ B|

|A ∩ B| = 20

So, 20 youths use both iPhone and Samsung.

To find the number of youths who use neither, we can use the fact that:

|A ∪ B ∪ C| = 1100

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

Plugging in the values we know, we get:

1100 = 150 + 770 + |C| - 20 - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

|C| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 200

Since the number of youths using both is 20, we have:

|A ∩ C| = |B ∩ C| = |A ∩ B ∩ C| = 0

So, we can simplify the equation to:

|C| = 200

Therefore, 200 youths use neither iPhone nor Samsung.

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Answer:

Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.

Step-by-step explanation:

To find the volume and surface area of a diversion tunnel, we can use the formulas for the volume and lateral surface area of a cylinder.

The volume of a cylinder is given by the formula:

V = πr^2h

Where:

V is the volume,

π is a mathematical constant approximately equal to 3.14159,

r is the radius of the cylinder, and

h is the height (or length) of the cylinder.

Substituting the given values:

r = 56 feet

h = 4,000 feet

V = π(56^2)(4,000)

V ≈ 3.14159 * 56^2 * 4,000

Calculating the volume:

V ≈ 9,839,916,800 cubic feet

The surface area of the lateral (curved) part of a cylinder is given by the formula:

A = 2πrh

Where:

A is the surface area,

π is a mathematical constant approximately equal to 3.14159,

r is the radius of the cylinder, and

h is the height (or length) of the cylinder.

Substituting the given values:

r = 56 feet

h = 4,000 feet

A = 2π(56)(4,000)

A ≈ 2 * 3.14159 * 56 * 4,000

Calculating the surface area:

A ≈ 1,000,530.9 square feet

Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.

Answer:

$42

Step-by-step explanation:

less than 8 is supposed to be 7 or less 6×7=$42

The element of A n B is { 7, 8}

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind.

For example, if the element of P is even numbers from 1 to 20 and element of Q is factor of 6 from 1 to 20 then we can say that set Q is a subset of set P.

The sign 'n' means intersection and this means what is common to two or more set.

If set A = { 1,2,5,7,8}

set B = { 6,7,8,9}

then we can see that 7 and 8 are common to both sides, then

A n B = { 7,8}

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\(given \: that \: its \: linear \\ m = \frac{15 - 3}{3 - 0} = \frac{12}{3} = 4 \)

\(b = y(0) = 3 \\ y = 4x + 3 \: \)

Answer:

D) y = 4x + 3

Step-by-step explanation:

   \(\sf \boxed{\bf y = mx +b}\)

Here, m is the slope and b is y intercept.

At y intercept, x = 0

         From the table, y intercept  = 3

Choose any two points from the table to find the slope.

(0 ,3)  & (3,15)

\(\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}\)

           \(\sf =\dfrac{15-3}{3-0}\\\\=\dfrac{12}{3}\\\\=4\)

m = 4 ; b = 3

 Equation of line:

                 y = 4x  + 3

To solve this question, we use the factor theorem, and using it, the polynomial function is:

\(f(x) = x^3 - 2x^2 - 3x + 6\)

------------------------------

The factor theorem means that if k is a root of f(x), f(k) = 0.

Thus, applying the factor theorem for this question, we have to choose the function for which: \(f(2) = 0, f(\sqrt{3}) = 0, f(-\sqrt{3}) = 0\)

------------------------------

Function 1:

\(f(x) = x^3 - 2x^2 - 3x + 6\)

Testing the values:

\(f(2) = 2^3 - 2(2)^2 - 3(2) + 6 = 8 - 8 - 6 + 6 = 0\)

\(f(\sqrt{3}) = \sqrt{3^3} - 2(\sqrt{3})^2 - 3\sqrt{3} + 6 = \sqrt{3^2\times3} - 6 - 3\sqrt{3} + 6 = 3\sqrt{3} - 3\sqrt{3} = 0\)

\(f(-\sqrt{3}) = -\sqrt{3^3} - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 = -\sqrt{3^2\times3} - 6 + 3\sqrt{3} + 6 = -3\sqrt{3} + 3\sqrt{3} = 0\)

Thus, since all three conditions are satisfied, \(f(x) = x^3 - 2x^2 - 3x + 6\) is the polynomial function.

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given the expression:

4^5 x 4^-7/4^-2

we are to fin what the above expression is equal to.

first one thing we must understand they all have same base which is 4

4^5 x 4^-7/4^-2

since they have the same base we will use the laws of indices of multiplication and division

the law of multiplication states that if the have have the same base, we add the powers while the laws of division states that if they have same base, we subtract the powers

so lets deal with tah of division first

4^5 x 4^-7-(-2)

4^5 x 4^-7+2

4^5 x 4^-5

using the law of multiplication

4^5+(-5)

4^5-5

4^0

therefore, the correct option is the first option which is 4^0

The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

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Answer:

80 - 66 = 14

Step-by-step explanation:

I have an assignment with this question

Answer: 6 cm, V=48π or V=150.8 cm³

It appears the question is asking for the radius, but below I have shown how to find the volume.

Step-by-step explanation:

The radius is half of the diameter. The diameter of the cone of 12 cm. Half of 12 is 6. Therefore, the radius is 6 cm.

The formula to find the volume of a cone is \(V=\pi r^2\frac{h}{3}\). Now that we have the radius from above, we can use that to plug into the equation along with the given height.

\(V=\pi (6^2)\frac{4}{3}\)                    [expand the exponent]

\(V=36\pi \frac{4}{3}\)                       [combine like terms]

\(V=48\pi\) or \(V=150.8 cm^3\)            

Answer:

$7075 or 7718

Step-by-step explanation:

91100-6200=84900

84900/11= 7718.18181818 or rounded= 7718

(This is if the december month doesnt count.)

84900/12=7075

(If december is included.)

Answer:

her monthly salary = 84900/12= 7075 dollars

Step-by-step explanation:

total earns= 91100 dollars

actual salary does not include bonus

her actually salary : 91100-6200= 84900

her monthly salary = 84900/12= 7075 dollars

The formula for y in terms of x and c is given as follows:

\(y = \frac{c^5}{\sqrt{x}}\)

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

An inverse proportional relationship is modeled as follows:

y = k/x.

In this problem, we have that y is inverse proportional to the square root of x, hence the equation is given as follows:

\(y = \frac{k}{\sqrt{x}}\)

When x = c², y = c^4, hence the constant k is obtained as follows:

\(c^4 = \frac{k}{\sqrt{c^2}}\)

k/c = c^4

k = c^5.

Hence the equation is:

\(y = \frac{c^5}{\sqrt{x}}\)

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The points on the surface z² = xy+ 1 which are closest to the point

(7, 11, 0) is x = 2 and y = 10.

The distance of any point on the surface from the point (7, 11, 0)  is

D(x, y) = { [ x -7]2 + [ y -11 ]2 + [ z -0 ]2 } 1/2

D(x, y) = { [ x -7]2 + [ y -11 ]2 +  z 2 } 1/2

D(x, y) = { [ x -7]2 + [ y -11 ]2 + z 2 } 1/2

D(x, y) = { [ x -7]2 + [ y -11 ]2 + x y +1 } 1/2

Now,

To minimize D  suffices to minimize

d (x ,y ) =  [ x -7]2 + [ y -11 ]2 + x y +1

∂ d / ∂ x =2 x + y - 14

∂ d / d y = 2 y +x - 22

Solving the system:

2x + y - 14 = 0   and    2y +x - 22 = 0   we get  for

x = 2  and for y = 10

The Hessian being 3 > 0  and  d²x  and  d²y positive makes sure that the points ( 2 , 10, √21 )  and   ( 2 , 10, -√21 )  are the points of interest

Complete Question:

Find the point(s) on the surface z2=xy+1 which are closest to the point

(7, 11, 0). List points as a comma-separated list, (e.g., (1,1,-1), (2, 0, -1),

(2,0, 3)).

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The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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Answer:

x= 1

Step-by-step explanation:

x = 1 is the axis of symmetric for the graph

if we draw a line parallel to the y axis one units to the right side of the origin we get the line of symmetry of the graph.

and since the line of symmetry is parallel to y axis and passes thru the point (1, 0) it's equation is x= 1

Answer: 4/15

Step-by-step explanation:

Answer:it will be D

Step-by-step explanation: because $100 + 4%=$100.4

The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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Answer: A because its always A

Step-by-step explanation:

The p-value can also be calculated using a t-distribution table or a statistical software package. Using a two-tailed test with 7 degrees of freedom and a significance level of 0.05, we obtain a p-value of 0.073.

How to solve the question?

To determine whether the fitness program has had a significant effect on reducing employee absenteeism, we need to conduct a hypothesis test.

Null hypothesis: The average number of absences before and after the fitness program are the same.

Alternative hypothesis: The average number of absences after the fitness program is less than before the program.

To test this hypothesis, we can use a one-tailed paired t-test with a significance level of 0.05. We will calculate the difference between the number of absences before and after the program for each employee, and then compute the mean and standard deviation of the differences. The t-test statistic will then be calculated as the mean difference divided by the standard deviation of the differences, multiplied by the square root of the sample size.

Using the given data, we calculate the differences and obtain the following results:

Employee Before After Difference (d) d²

1 8 7 -1 1

2 7 3 -4 16

3 8 2 -6 36

4 8 4 -4 16

5 6 5 -1 1

6 7 10 3 9

7 6 4 -2 4

8 8 9 1 1

Mean difference (d-bar) = -1.25

Standard deviation of differences (s) = 3.27

Sample size (n) = 8

The t-test statistic can now be calculated as:

t = (d-bar / (s / √(n))) = (-1.25 / (3.27 / √(8))) = -1.63

The degrees of freedom for the t-test is n-1 = 7, which can be used to obtain the p-value from a t-table or calculator. Using a one-tailed test with a significance level of 0.05 and 7 degrees of freedom, the critical t-value is -1.895.

Since our calculated t-value (-1.63) is greater than the critical t-value (-1.895), we fail to reject the null hypothesis. In other words, we do not have sufficient evidence to conclude that the fitness program has resulted in a significant reduction in employee absenteeism.

The p-value can also be calculated using a t-distribution table or a statistical software package. Using a two-tailed test with 7 degrees of freedom and a significance level of 0.05, we obtain a p-value of 0.073. Since this p-value is greater than the significance level, we again fail to reject the null hypothesis.

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Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

             {4,  6}

      C) -  The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

MAKE A PLAN:

List The OUTCOMES for EACH EVENT and their COMBINATIONS:

        a) -  EVENT  "A":  {2, 4, 6, 8}

               EVENT "B":   {3, 4, 5, 6}

               EVENT "A" or "B": {2, 3, 4, 5, 6, 8}

        b) - EVENT "A"  or "B":  {4, 6}

        c) -  The COMPLEMENT of the EVENT "A":  {1, 3, 5, 7}

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

            {4,  6}

      C) - The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

I hope this helps!

Answer:

0.0806

Step-by-step explanation:

From the given information:

Number of toss = 50

The probability of having a head = 1/2 = 0.5

The Probability of 8th head occur on 12th toss can be computed as :

Pr(8th head occur on 12th toss) = Pr(7 heads in 11 toss) × P(8th head on 12th toss)

Pr(8th head occur on 12th toss) =  C(11,7) × 0.5⁷ × (1 - 0.5)⁴ * 0.5

Pr(8th head occur on 12th toss) = \(\dfrac{11!}{7!(11-7)!}\) × 0.5⁷ × (1 - 0.5)⁴ × 0.5

Pr(8th head occur on 12th toss) =  0.0806

Answer:

The probability of 8th heads,

That is occurred on 12th toss.

Step-by-step explanation:

A coin is tossed 50 times.

There are two possible outcomes of occurring a head or tail.

Probability of occurring head = no.of head/ possible outcomes

                                                    = 1/2

Total number of tossing a coin= 50 times

Probability of 8th heads occurs on 12th toss:

                                                         12C8 (1/2)8 (1/2)9 (1/2)10 (1/2)11 (1/2)12

                                 =         12C8  (1/2)8+9+10+11+12

                                                    = 12C8  (1/2)50

                                  = 12C8   / 250

                                                       = 495 / 1125899906842624

                                  = 4396.48317752 x 10-16

This is the probability of 8th heads,

That is occurred on 12th toss.